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564 lines
18 KiB
C++
564 lines
18 KiB
C++
/* *************************************************************************/
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/* File: surfacegeom.cpp */
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/* Author: Michael Neunteufel */
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/* Date: Jun. 2020 */
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/* *************************************************************************/
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#include <meshing.hpp>
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namespace netgen
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{
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SurfaceGeometry :: SurfaceGeometry()
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{
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//identity
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func = [](Point<2> p) { return Vec<3>(p[0],p[1],0.0); };
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}
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SurfaceGeometry :: SurfaceGeometry(function<Vec<3>(Point<2>)> _func) : func(_func)
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{
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;
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}
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SurfaceGeometry :: SurfaceGeometry(const SurfaceGeometry& geom) : func(geom.func), eps(geom.eps)
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{
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;
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}
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void SurfaceGeometry :: CalcHesse(double u, double v, Vec<3>& f_uu, Vec<3>& f_vv, Vec<3>& f_uv) const
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{
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Point<2> p = Point<2>(u,v);
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double pr = p[0]+eps;
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double pl = p[0]-eps;
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double prr = p[0]+2*eps;
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double pll = p[0]-2*eps;
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auto dr = GetTangentVectors( pr, v );
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auto dl = GetTangentVectors( pl, v );
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auto drr = GetTangentVectors( prr, v );
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auto dll = GetTangentVectors( pll, v );
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f_uu = (1.0/(12.0*eps)) * (8.0*dr[0]-8.0*dl[0]-drr[0]+dll[0]);
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f_uv = (1.0/(12.0*eps)) * (8.0*dr[1]-8.0*dl[1]-drr[1]+dll[1]);
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pr = p[1]+eps;
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pl = p[1]-eps;
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prr = p[1]+2*eps;
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pll = p[1]-2*eps;
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GetTangentVectors(u, pr, dr);
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GetTangentVectors(u, pl, dl);
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GetTangentVectors(u, prr, drr);
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GetTangentVectors(u, pll, dll);
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f_vv = (1.0/(12.0*eps)) * (8.0*dr[1]-8.0*dl[1]-drr[1]+dll[1]);
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}
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Array<Vec<3>> SurfaceGeometry :: GetTangentVectors(double u, double v) const
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{
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Array<Vec<3>> tang(2);
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Point<2> pru = Point<2>(u+eps,v);
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Point<2> plu = Point<2>(u-eps,v);
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Point<2> prru = Point<2>(u+2*eps,v);
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Point<2> pllu = Point<2>(u-2*eps,v);
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Point<2> prv = Point<2>(u,v+eps);
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Point<2> plv = Point<2>(u,v-eps);
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Point<2> prrv = Point<2>(u,v+2*eps);
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Point<2> pllv = Point<2>(u,v-2*eps);
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tang[0] = 1/(12.0*eps)*( 8.0*func(pru) - 8.0*func(plu) - func(prru) + func(pllu) );
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tang[1] = 1/(12.0*eps)*( 8.0*func(prv) - 8.0*func(plv) - func(prrv) + func(pllv) );
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return tang;
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}
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void SurfaceGeometry :: GetTangentVectors(double u, double v, Array<Vec<3>>& tang) const
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{
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Point<2> pru = Point<2>(u+eps,v);
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Point<2> plu = Point<2>(u-eps,v);
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Point<2> prru = Point<2>(u+2*eps,v);
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Point<2> pllu = Point<2>(u-2*eps,v);
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Point<2> prv = Point<2>(u,v+eps);
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Point<2> plv = Point<2>(u,v-eps);
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Point<2> prrv = Point<2>(u,v+2*eps);
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Point<2> pllv = Point<2>(u,v-2*eps);
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tang[0] = 1/(12.0*eps)*( 8.0*func(pru) - 8.0*func(plu) - func(prru) + func(pllu) );
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tang[1] = 1/(12.0*eps)*( 8.0*func(prv) - 8.0*func(plv) - func(prrv) + func(pllv) );
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}
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Vec<3> SurfaceGeometry :: GetNormal(int surfind, const Point<3> & p, const PointGeomInfo* gi) const
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{
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Array<Vec<3>> tang = GetTangentVectors(gi->u, gi->v);
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auto normal = Cross(tang[0], tang[1]);
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normal.Normalize();
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return normal;
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}
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PointGeomInfo SurfaceGeometry :: ProjectPoint(int surfind, Point<3> & p) const
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{
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throw Exception("In SurfaceGeometry::ProjectPoint");
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}
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void SurfaceGeometry :: ProjectPointEdge (int surfind, int surfind2, Point<3> & p,
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EdgePointGeomInfo* gi) const
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{
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if (gi == nullptr)
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throw Exception("In SurfaceGeometry::ProjectPointEdge: gi is nullptr");
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throw Exception("In SurfaceGeometry::ProjectPointEdge: not implemented");
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}
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bool SurfaceGeometry :: ProjectPointGI (int surfind, Point<3> & p, PointGeomInfo & gi) const
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{
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Array<Vec<3>> tangs(2);
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Vec<3> diff, f_uu, f_vv, f_uv;
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Vec<2> r, dx;
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double norm_r, det, energy=0.0, new_energy=0.0, alpha=2.0,u=0.0,v=0.0,maxerr=1e-16;
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Mat<2,2> mat, inv;
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int num=0, maxit=25;
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double damping=0.5;
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//Solve minimization problem
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// argmin_(u,v) 0.5*\| f(u,v)-p\|^2
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//via Neton's method:
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// F(u,v) = ( (f(u,v)-p)*f_u(u,v), (f(u,v)-p)*f_v(u,v))^T = (0,0)^T
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//Stiffness matrix
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// F'(u,v) = ( f_u*f_u + (f-p)*f_uu, f_v*f_u + (f-p)*f_uv, f_v*f_u + (f-p)*f_uv, f_v*f_v + (f-p)*f_vv )
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do
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{
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num++;
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GetTangentVectors(gi.u, gi.v,tangs);
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diff = func(Point<2>(gi.u, gi.v)) - Vec<3>(p);
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energy = diff.Length2();
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r = Vec<2>( diff*tangs[0], diff*tangs[1] );
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norm_r = r.Length2();
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CalcHesse(gi.u, gi.v, f_uu, f_vv, f_uv);
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mat(0,0) = tangs[0]*tangs[0] + diff*f_uu;
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mat(1,0) = mat(0,1) = tangs[0]*tangs[1]+diff*f_uv;
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mat(1,1) = tangs[1]*tangs[1]+diff*f_vv;
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CalcInverse(mat,inv);
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dx = inv*r;
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//Linesearch
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alpha = 2.0;
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do
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{
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alpha /= 2.0;
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u = gi.u - min(1.0,alpha*damping*num)*dx[0];
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v = gi.v - min(1.0,alpha*damping*num)*dx[1];
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diff = func(Point<2>(u, v)) - Vec<3>(p);
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new_energy = diff.Length2();
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}
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while (alpha > 1e-10 && new_energy > energy+1e-14);
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if (alpha <= 1e-10)
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throw Exception("In SurfaceGeometry::ProjectPointGI: Linesearch min alpha reached!");
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gi.u = u;
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gi.v = v;
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}
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while ( norm_r > maxerr && num < maxit);
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//Stay in reference domain [0,1]^2
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if (gi.u < 0 || gi.u > 1 || gi.v < 0 || gi.v > 1)
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{
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cout << "Warning: Projected point outside [0,1]^2: u=" << gi.u << ",v=" << gi.v <<". Setting back." << endl;
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gi.u = min(max(gi.u,0.0),1.0);
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gi.v = min(max(gi.v,0.0),1.0);
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}
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p = Point<3>(func(Point<2>(gi.u,gi.v)));
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if (num == maxit)
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{
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//cout << "In SurfaceGeometry::ProjectPointGI: Newton did not converge" << endl;
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throw Exception("In SurfaceGeometry::ProjectPointGI: Newton did not converge");
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}
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return true;
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}
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bool SurfaceGeometry :: CalcPointGeomInfo(int surfind, PointGeomInfo& gi, const Point<3> & p3) const
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{
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throw Exception("In SurfaceGeometry::CalcPointGeomInfo: not implemented");
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return false;
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}
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void SurfaceGeometry :: PointBetweenEdge(const Point<3> & p1, const Point<3> & p2, double secpoint, int surfi1, int surfi2, const EdgePointGeomInfo & ap1, const EdgePointGeomInfo & ap2, Point<3> & newp, EdgePointGeomInfo & newgi) const
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{
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newgi.u = ap1.u+secpoint*(ap2.u-ap1.u);
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newgi.v = ap1.v+secpoint*(ap2.v-ap1.v);
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newgi.edgenr = ap1.edgenr;
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newgi.body = -1;
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newgi.dist = -1.0;
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newp = Point<3>(func(Point<2>(newgi.u, newgi.v)));
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}
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void CheckForBBBPnt(const Array<Point<3>>& bbbpts, const Point<3>& pnt, Array<bool>& found, Array<PointIndex>& indbbbpts, const Array<PointIndex>& pids)
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{
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for (int k = 0; k < bbbpts.Size(); k++)
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{
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auto diff = pnt - bbbpts[k];
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if(diff.Length2() < 1e-14)
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{
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found[k] = true;
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indbbbpts[k] = pids[pids.Size()-1];
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}
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}
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}
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void CheckForSingularity(const Array<Point<3>>& hppoints, const Point<3>& pnt, const Array<float>& hpptsfac, shared_ptr<Mesh> & mesh, const Array<PointIndex>& pids)
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{
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for (int k = 0; k < hppoints.Size(); k++)
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{
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auto diff = pnt - hppoints[k];
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if(diff.Length2() < 1e-14)
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{
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(*mesh)[pids[pids.Size()-1]].Singularity(hpptsfac[k]);
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}
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}
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}
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void SurfaceGeometry :: PointBetween(const Point<3> & p1, const Point<3> & p2, double secpoint,
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int surfi,
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const PointGeomInfo & gi1,
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const PointGeomInfo & gi2,
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Point<3> & newp, PointGeomInfo & newgi) const
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{
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newgi.u = gi1.u+secpoint*(gi2.u-gi1.u);
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newgi.v = gi1.v+secpoint*(gi2.v-gi1.v);
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newgi.trignum = -1;
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newp = Point<3>(func(Point<2>(newgi.u, newgi.v)));
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//newp = p1+secpoint*(p2-p1);
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//ProjectPointGI(surfi, newp, newgi);
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}
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int SurfaceGeometry :: GenerateStructuredMesh(shared_ptr<Mesh> & mesh, bool quads, int nx, int ny, bool flip_triangles, const Array<Point<3>>& bbbpts, const Array<string>& bbbnames, const Array<Point<3>>& hppoints, const Array<float>& hpptsfac, const Array<string>& hpbnd, const Array<float>& hpbndfac, Array<double> layer_thickness[4], bool layer_quad)
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{
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mesh->SetDimension(3);
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Array<bool> found(bbbpts.Size());
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found = false;
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Array<PointIndex> indbbbpts(bbbpts.Size());
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int numx = nx;
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int numy = ny;
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size_t total_layer_el[4] = {layer_thickness[0].Size(), layer_thickness[1].Size(), layer_thickness[2].Size(), layer_thickness[3].Size()};
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double interior_x = 1.0;
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double interior_y = 1.0;
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for(double scale : layer_thickness[0])
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interior_x -= scale;
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for(double scale : layer_thickness[2])
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interior_x -= scale;
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for(double scale : layer_thickness[1])
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interior_y -= scale;
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for(double scale : layer_thickness[3])
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interior_y -= scale;
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auto AddPoint = [&] (double offsetx, double offsety, Array<PointIndex> & pids, Array<PointGeomInfo> & pgis)
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{
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PointGeomInfo pgi;
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pgi.trignum = -1;
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pgi.u = offsetx;
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pgi.v = offsety;
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Point<3> pnt = Point<3>(func(Point<2>(pgi.u,pgi.v)));
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pids.Append(mesh->AddPoint(pnt));
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pgis.Append(pgi);
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CheckForBBBPnt(bbbpts, pnt, found, indbbbpts, pids);
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CheckForSingularity(hppoints, pnt, hpptsfac, mesh, pids);
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};
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auto InternalLoop = [&] (double offsety, Array<PointIndex> & pids, Array<PointGeomInfo> & pgis)
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{
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int j = 0;
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double offsetx = 0.0;
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for(int l=0; l < layer_thickness[0].Size(); l++,j++)
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{
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AddPoint(offsetx+layer_thickness[0][l]*double(j-l), offsety, pids, pgis);
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offsetx += layer_thickness[0][l];
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}
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for(;j <= nx-total_layer_el[2]; j++)
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AddPoint(offsetx + interior_x*double(j-total_layer_el[0])/(nx-total_layer_el[0]-total_layer_el[2]), offsety, pids, pgis);
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offsetx += interior_x;
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int startj = j;
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for(int l=0; l < layer_thickness[2].Size(); l++, j++)
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{
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AddPoint(offsetx+layer_thickness[2][layer_thickness[2].Size()-1-l]*double(j-startj-l+1), offsety, pids, pgis);
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offsetx += layer_thickness[2][layer_thickness[2].Size()-1-l];
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}
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};
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Array<PointIndex> pids;
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Array<PointGeomInfo> pgis;
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int i = 0;
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double offsety = 0.0;
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for(int k=0; k < layer_thickness[1].Size(); k++,i++)
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{
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InternalLoop(offsety, pids, pgis);
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offsety += layer_thickness[1][k];
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}
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for(; i <= ny-total_layer_el[3]; i++)
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{
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InternalLoop(offsety, pids, pgis);
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offsety += interior_y/(ny-total_layer_el[1]-total_layer_el[3]);
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}
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offsety -= interior_y/(ny-total_layer_el[1]-total_layer_el[3]);
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for(int k=0; k < layer_thickness[3].Size(); k++,i++)
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{
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offsety += layer_thickness[3][layer_thickness[3].Size()-1-k];
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InternalLoop(offsety, pids, pgis);
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}
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for (bool f : found)
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if (!f)
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throw Exception("In SurfaceGeometry :: GenerateMesh: bbbpts not resolved in mesh.");
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FaceDescriptor fd;
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fd.SetSurfNr(1);
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fd.SetDomainIn(1);
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fd.SetDomainOut(0);
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fd.SetBCProperty(1);
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mesh->AddFaceDescriptor(fd);
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for(int i=0; i < numy; i++)
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{
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for(int j=0; j < numx; j++)
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{
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int base = i * (numx+1) + j;
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if (quads || (layer_quad && i < total_layer_el[1]) || (layer_quad && i > numy-1-total_layer_el[3]) || (layer_quad && j < total_layer_el[0]) || (layer_quad && j > numx-1-total_layer_el[2]) )
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{
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int pnum[4] = {base,base+1,base+numx+2,base+numx+1};
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Element2d el = Element2d(QUAD);
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for (int i = 0; i < 4; i++)
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{
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el[i] = pids[pnum[i]];
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el.GeomInfoPi(i+1) = pgis[pnum[i]];
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}
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el.SetIndex(1);
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mesh->AddSurfaceElement(el);
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}
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else
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{
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Array<int> pnum1(3);
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Array<int> pnum2(3);
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if (flip_triangles)
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{
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pnum1[0] = base;
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pnum1[1] = base+1;
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pnum1[2] = base+numx+2;
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pnum2[0] = base;
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pnum2[1] = base+numx+2;
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pnum2[2] = base+numx+1;
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}
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else
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{
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pnum1[0] = base;
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pnum1[1] = base+1;
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pnum1[2] = base+numx+1;
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pnum2[0] = base+1;
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pnum2[1] = base+numx+2;
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pnum2[2] = base+numx+1;
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}
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Element2d el = Element2d(TRIG);
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for (int i = 0; i < 3; i++)
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{
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el[i] = pids[pnum1[i]];
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el.GeomInfoPi(i+1) = pgis[pnum1[i]];
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}
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el.SetIndex(1);
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mesh->AddSurfaceElement(el);
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for (int i = 0; i < 3; i++)
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{
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el[i] = pids[pnum2[i]];
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el.GeomInfoPi(i+1) = pgis[pnum2[i]];
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}
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mesh->AddSurfaceElement(el);
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}
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}
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}
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Segment seg;
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seg.si = 1;
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seg.edgenr = 1;
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seg.epgeominfo[0].edgenr = 0;
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seg.epgeominfo[1].edgenr = 0;
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//for hp refinement
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seg.singedge_left = 0;
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seg.singedge_right = 0;
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for (size_t i=0; i < hpbnd.Size(); i++)
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{
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if (hpbnd[i] == "bottom")
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{
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seg.singedge_left = hpbndfac[i];
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seg.singedge_right = hpbndfac[i];
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}
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}
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// needed for codim2 in 3d
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seg.edgenr = 1;
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for(int i=0; i < numx; i++)
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{
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seg[0] = pids[i];
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seg[1] = pids[i+1];
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seg.geominfo[0] = pgis[i];
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seg.geominfo[1] = pgis[i+1];
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seg.epgeominfo[0].u = pgis[i].u;
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seg.epgeominfo[0].v = pgis[i].v;
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seg.epgeominfo[0].edgenr = seg.edgenr;
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seg.epgeominfo[1].u = pgis[i+1].u;
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seg.epgeominfo[1].v = pgis[i+1].v;
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seg.epgeominfo[1].edgenr = seg.edgenr;
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mesh->AddSegment(seg);
|
|
}
|
|
|
|
seg.si = 2;
|
|
seg.edgenr = 2;
|
|
seg.singedge_left = 0;
|
|
seg.singedge_right = 0;
|
|
|
|
for (size_t i=0; i < hpbnd.Size(); i++)
|
|
{
|
|
if (hpbnd[i] == "right")
|
|
{
|
|
seg.singedge_left = hpbndfac[i];
|
|
seg.singedge_right = hpbndfac[i];
|
|
}
|
|
}
|
|
|
|
for(int i=0; i<numy; i++)
|
|
{
|
|
seg[0] = pids[i*(numx+1)+numx];
|
|
seg[1] = pids[(i+1)*(numx+1)+numx];
|
|
|
|
seg.geominfo[0] = pgis[i*(numx+1)+numx];
|
|
seg.geominfo[1] = pgis[(i+1)*(numx+1)+numx];
|
|
seg.epgeominfo[0].u = pgis[i*(numx+1)+numx].u;
|
|
seg.epgeominfo[0].v = pgis[i*(numx+1)+numx].v;
|
|
seg.epgeominfo[0].edgenr = seg.edgenr;
|
|
seg.epgeominfo[1].u = pgis[(i+1)*(numx+1)+numx].u;
|
|
seg.epgeominfo[1].v = pgis[(i+1)*(numx+1)+numx].v;
|
|
seg.epgeominfo[1].edgenr = seg.edgenr;
|
|
|
|
mesh->AddSegment(seg);
|
|
}
|
|
|
|
seg.si = 3;
|
|
seg.edgenr = 3;
|
|
seg.singedge_left = 0;
|
|
seg.singedge_right = 0;
|
|
|
|
for (size_t i=0; i < hpbnd.Size(); i++)
|
|
{
|
|
if (hpbnd[i] == "top")
|
|
{
|
|
seg.singedge_left = hpbndfac[i];
|
|
seg.singedge_right = hpbndfac[i];
|
|
}
|
|
}
|
|
|
|
for(int i=0; i<numx; i++)
|
|
{
|
|
seg[0] = pids[numy*(numx+1)+i+1];
|
|
seg[1] = pids[numy*(numx+1)+i];
|
|
|
|
seg.geominfo[0] = pgis[numy*(numx+1)+i+1];
|
|
seg.geominfo[1] = pgis[numy*(numx+1)+i];
|
|
seg.epgeominfo[0].u = pgis[numy*(numx+1)+i+1].u;
|
|
seg.epgeominfo[0].v = pgis[numy*(numx+1)+i+1].v;
|
|
seg.epgeominfo[0].edgenr = seg.edgenr;
|
|
seg.epgeominfo[1].u = pgis[numy*(numx+1)+i].u;
|
|
seg.epgeominfo[1].v = pgis[numy*(numx+1)+i].v;
|
|
seg.epgeominfo[1].edgenr = seg.edgenr;
|
|
|
|
mesh->AddSegment(seg);
|
|
}
|
|
|
|
seg.si = 4;
|
|
seg.edgenr = 4;
|
|
seg.singedge_left = 0;
|
|
seg.singedge_right = 0;
|
|
for (size_t i=0; i < hpbnd.Size(); i++)
|
|
{
|
|
if (hpbnd[i] == "left")
|
|
{
|
|
seg.singedge_left = hpbndfac[i];
|
|
seg.singedge_right = hpbndfac[i];
|
|
}
|
|
}
|
|
|
|
|
|
for(int i=0; i<numy; i++)
|
|
{
|
|
seg[0] = pids[(i+1)*(numx+1)];
|
|
seg[1] = pids[i*(numx+1)];
|
|
|
|
seg.geominfo[0] = pgis[(i+1)*(numx+1)];
|
|
seg.geominfo[1] = pgis[i*(numx+1)];
|
|
seg.epgeominfo[0].u = pgis[(i+1)*(numx+1)].u;
|
|
seg.epgeominfo[0].v = pgis[(i+1)*(numx+1)].v;
|
|
seg.epgeominfo[0].edgenr = seg.edgenr;
|
|
seg.epgeominfo[1].u = pgis[i*(numx+1)].u;
|
|
seg.epgeominfo[1].v = pgis[i*(numx+1)].v;
|
|
seg.epgeominfo[1].edgenr = seg.edgenr;
|
|
|
|
mesh->AddSegment(seg);
|
|
}
|
|
|
|
mesh->SetCD2Name(1, "bottom");
|
|
mesh->SetCD2Name(2, "right");
|
|
mesh->SetCD2Name(3, "top");
|
|
mesh->SetCD2Name(4, "left");
|
|
|
|
for (int i = 0; i < bbbpts.Size(); i++)
|
|
{
|
|
Element0d el;
|
|
el.pnum = indbbbpts[i];
|
|
el.index = i+1;
|
|
mesh->pointelements.Append(el);
|
|
mesh->SetCD3Name(i+1, bbbnames[i]);
|
|
}
|
|
|
|
mesh->Compress();
|
|
mesh->UpdateTopology();
|
|
|
|
return 0;
|
|
}
|
|
|
|
};
|